﻿Binding of Electrons by Atoms. 197 



where W is positive, and represents the total energy, and 

 the p's are the momenta. 

 We have thus 



p. d = const. = -i-, 

 Lit 



sin 2 0' 



sin 2 

 being clearly positive, 



The phase-integral for p 2 is 



nji = \p, d0 = 2\ d0 . \J /3 2 - 



the limits being the suitable values of for which ^ 2 = 0. 

 The factor 2 represents the double journey in this co- 

 ordinate, 



sin^=^, 



where ifr is one of the limits, and the other admissible value, 

 for a real integral, is 7r — -v/r. Thus 



n 2 h = 2^ d0 V£^3~7sin 2 







Write 







P 2 





w = sm^ &) + — o cos w > 





2?3 



and we have 





n 2 h 



A Q /3 2 — ^ 3 2 f ff/2 COS 2 0) di&> 

 — ^P 2 fi>2 ? 



^ 3 -° sin 2 o)+- 2 cos 2 o) 





^3 2 



or with tan co = t, 



n q h = -h; 



ft J. (1+^(1^) 



= 4 J 8(tan- 1 *-§tan- 1 %'l 



